The role of an MP is to represent the wishes of his constituency, I'm not sure about how that would result in banning the French etc but it has set MPs against the party line (e.g. Goldsmith). It's usually only in unique circumstances that an MP can gauge an attitude to a specific issue, for example closing a hospital. The referendum has given each MP a good idea of what their constituents decided, so you could argue that they will follow this.
The role of the MP is not to represent the wishes of his constituency but to review legislation and to represent local interests in Parliament at Westminster. In the House of Commons, MPs scrutinise legislation, attend debates and committees, and generally protect, advocate and promote the interests of their constituency at a national level. An MP represents all of their constituency whether they voted for that MP or not or for that matter whether constituents voted leave/or remain! Given that, if MP's consider leaving the EU is against the national interest and against the interests of all their constituents then that is their call. That is why we vote for them that is how our British system of government works.